Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

Hi,

I am writing the following code and MAPLE is giving me operator error. Please help (file: doubt_6.mw)

d2:=100000000

for m in set_m do
    for n in set_n do
        SOL1 := fsolve({ODE11, ODE12}, {N, t__2});
        N1:=eval(N,SOL1);
        t_2_1 :=eval(t__2,SOL1);
        T_1:= eval(T, [lambda = 3, a = 300, b = .15, c = .25, A__m = 300, A__d = 150, A__r = 50,C__m = 4, P__m = 8, P__d = 10, 
        P__r = 12, theta__m = .15, theta__d = .12, theta__r = 0.5e-1, h__m = .2, h__d = .3, h__r = .5, i__m = .1, i__d = .1, 
        i__r = .1, i__om = .1, i__OD = .15, i__c = .3, i__e = .2, M = 2, alpha = 0.2e-1, t__2 = t_2_1]):
        t_31:= T_1 /m ;
        t_41:= T_1 /(m*n) ;
        if (N1<=t_41 and 2>=t_31) then
            d1:= eval(TCS__1, [lambda = 3, a = 300, b = .15, c = .25, A__m = 300, A__d = 150, A__r = 50, C__m = 4, P__m = 8, 
            P__d = 10, P__r = 12, theta__m = .15, theta__d = .12, theta__r = 0.5e-1, h__m = .2, h__d = .3, h__r = .5, i__m = .1, 
            i__d = .1, i__r = .1, i__om = .1, i__OD = .15, i__c = .3, i__e = .2, M = 2, alpha = 0.2e-1, t__2=t_2_1, N=N1]):
            if (d1<= d2) then
                d2:= d1;
                print("Value is updated",d2,N1,t_2_1,"for",m,n)
            end if
        end if    
        print(N1,t_2_1,t_31,t_41,d1,m,n)
    end do
end do

 

Thanks in advance

 

[[p__jb = (Typesetting[delayDotProduct](c__a . ((rho*(-1+alpha)*t__a-alpha*t__b)/(t__b*t__a)), t__b, true)*t__a+((c__b+`p__-jb`)*alpha-c__b-t__b-`p__-jb`)*t__a-alpha*t__b*(c__b+`p__-jb`))/((2*alpha-2)*t__a-2*alpha*t__b)]]

hi

I'm working on my thesis,to solve a particular problem,I created a 84*84 matrix in Matlab.

I want to calculate the determinat of that matrix in maple,so from tools>assistance>import date added this matrix in maple.

every thing seems to be ok but when i want to caculate the determinant this error apears :

 Error, (in LinearAlgebra:-Determinant) matrix must be square

does anybody know what is the problem here?

Also sorry for my weak English 

and it's worth mentioning that I'm a beginner in maple programming 

thank you

 

 

doubt5.mw

Hi I want to run the following algorithm in code edit region:

for m in set_m do
    for n in set_n do
      solve for N solving ODE11 and ODE12 simultaneously
      solve for t_2 solving ODE11 and ODE12 simultaneouly
      find t__3 and t__4
      if (N<=t_4 and M>=t_3) then
        d1= TCS__1 using n,m,t__2 and N
          if (d1< d2)
            d2=d1
            print(d2,m,n,N,t_2)
    end do
end do
 

But I am struck for to how to extract N and t__2 from SOL1 in code edit region

SOL1 := fsolve({ODE11, ODE12}, {N, t__2});

Thanks in advance

doubt4.mw

Hi, As shown in the figure(red color). I am not able to understand why Exp(0) is not showing as 1. As evaluating rules of maple says that it evaluates everything till it gets unassigned variables.

Do I am doing something wrong? There is a link to the file. 

Thanks in advance

doubt_3.mw

Hi, I am trying to do a simple think like

od2 := diff(x^3, x)+v+2 = 0

od3 := diff(v^2, v)+x+4 = 0

solve({(1),(2)},{x,v})

 

but with my code,  I am doing the exact same but getting the following error

Error, invalid input: solve expects its 1st argument, eqs, to be of type {`and`, `not`, `or`, algebraic, relation(algebraic), ({list, set})({`and`, `not`, `or`, algebraic, relation(algebraic)})}, but received {[1316.872428*(-0.1500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+3.000000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-3.000000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(int(.2*(.1*t+1)*i__m2(t), t = 0 .. t__2))/N^.98-11.76000000/(N^.98*((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2))+1185.185185*(-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-6.0000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))/(N^.98*((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2))+6.00*(-75.50000000*N^2.02+45.45000000*N^1.02+306.00*N^0.2e-1)/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)-1.200000000/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)-9.6*(-75.37500000*N^3.02+45.30000000*N^2.02+303.00*N^1.02)/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)] = 0, [-650*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2+65843.62140*N^0.2e-1*(-0.6750000000e-3*t__2^2-0.1350000000e-1*t__2+0.7500000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`-0.9000000000e-1-0.1500000000e-1*t__2*(0.900e-1*t__2+.90)+3.000000*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.900e-1*t__2+.90)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.6914062500e-6*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.6914062500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.1464843750e-7*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.1464843750e-7*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.1064062500e-3*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.1064062500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(int(.2*(.1*t+1)*i__m2(t), t = 0 .. t__2))+65843.62140*N^0.2e-1*(-0.1500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+3.000000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-3.000000)*(-0.5625000000e-3*t__2^2-0.1125000000e-1*t__2+0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`-0.7500000000e-1-0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(int(.2*(.1*t+1)*i__m2(t), t = 0 .. t__2))+13168.72428*N^0.2e-1*(-0.1500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+3.000000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.2250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.2304687500e-6*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.3662109374e-8*t__2^4*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^4*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.5320312500e-4*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-3.000000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(.1*t__2+1)*i__m2(t__2)+588.0000000*N^0.2e-1*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2+.60*(98765.43210*N^0.2e-1*(-0.5859375000e-5*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.5859375000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.9796875000e-3*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.9796875000e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))*(0.900e-1*t__2+.90)+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.900e-1*t__2+.90)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*(0.5625000000e-3*t__2^2+0.1125000000e-1*t__2-0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+0.7500000000e-1+0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+98765.43210*N^0.2e-1*(-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-6.0000)*(-0.5625000000e-3*t__2^2-0.1125000000e-1*t__2+0.6250000000e-2*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`-0.7500000000e-1-0.1250000000e-1*t__2*(0.900e-1*t__2+.90))*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+i__m2(t__2))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)-.60*(98765.43210*N^0.2e-1*(-0.1953125000e-5*t__2^3*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^3*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+0.4898437500e-3*t__2^2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)^2*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-0.7500000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+6.0000*exp(0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))-6.0000)*exp(-0.1250000000e-1*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6))+int(i__m2(t), t = 0 .. t__2))*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-(0.1500000000e-2*T^2+0.3000000000e-1*T)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-6.00*(-25.00000000*N^3.02+22.50000000*N^2.02+300*N^1.02)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-.1700000000*T*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-2.4*(.1000000000*T-.2000000000)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-4*(0.1562500000e-3*T^2+0.1250000000e-1*T)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2-12.0*(0.2500000000e-1*T-.1000000000*N)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2+9.6*(-18.75000000*N^4.02+15.00000000*N^3.02+150*N^2.02)*(0.3750000000e-2*t__2^2+0.7500000000e-1*t__2-0.4166666667e-1*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+3/2+(1/12)*t__2*(0.900e-1*t__2+.90))/((1/12)*t__2*(0.450e-1*t__2^2+.90*t__2-.50*`#msup(msub(mi("\`t"),mi("2\`")),mn("2"))`+6)+t__2)^2] = 0}

 

Please help

Thanks in advance 

Hi, I am working on a bification diagram and was wondering if there is a way to plot the stable and unstable curves onto one figure.

I have two curves, if the eq1<eq2 I would like to indicate when this happens, with a dashed line.

When eq1>eq3 I would like to indicate this with a soild line.

implicitplot, x[m] vs x[u] with axis[2]=[mode=log] 

r:=0.927: K:=1.8182*10^8:d[v]:=0.0038:d[u]:=2: delta:=1: p[m]:=2.5: M:=10^4: p[e]:=0.4: d[e]:=0.1: d[t]:=5*10^(-9): omega:=2.042: b:=1000: h[e]:=1000:h[u]:=1:h[v]:=10^4:

eq1 := r*d[t]*h[e]*x[u]^3+(r*h[e]*(-K*d[t]+d[t]*h[v]+d[e])+r*p[e]*x[m])*x[u]^2+(r*h[e]*(-K*d[t]*h[v]-K*d[e]+d[e]*h[v])+K*p[e]*(d[u]-r)*x[m])*x[u]-r*K*h[e]*d[e]*h[v];

eq2 := (d[t]*x[u]+d[e])*(2*r*x[u]/K+d[u]*p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e])*(h[e]+p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e]))))-r)+d[u]*h[e]*x[u]*(p[e]*h[v]*x[m]/(h[v]+x[u])^2-d[t]*p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e])))/(h[e]+p[e]*x[m]*x[u]/((h[v]+x[u])*(d[t]*x[u]+d[e])))^2

Hi, am trying to differentiate the following eq w.r.t t2 and N. But in t2 I am getting zero and in wrt N, an Error (non-algebraic expressions cannot be differentiated). But according to the article, I am following expression should come.

I am differentiating following

TCS := proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc

ode5 := diff(proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc, t__2) = 0

ode6 := diff(proc (N, T, m, n) options operator, arrow; piecewise(M <= t__3 and N <= t__4, TCS__1, M <= t__3 and t__4 < N, TCS__2, t__3 <= M and N <= t__4, TCS__3, `t__3 ` <= M and t__4 < N, TCS__4) end proc, N) = 0

Error, non-algebraic expressions cannot be differentiated
 

following are the pre-requisite to use above (also in the attachment doubt_2.mw)

i__m1(t) = ((-c*t^2*theta__m^2+b*t*theta__m^2+2*c*t*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t)

i__m2(t) = (-(-c*t^2*theta__m^2+b*t*theta__m^2+2*c*t*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(-theta__m*t)

TC__m := A__m/(t__1+t__2)+(int(h__m*(i__m*t+1)*i__m1(t), t = 0 .. t__1))*(int(h__m*(i__m*t+1)*i__m2(t), t = 0 .. t__2))+P__m*I__om*m*(-(1/3)*a*c*N^alpha*M^3+(1/2)*a*b*N^alpha*M^2+a*N^alpha*M)/(t__1+t__2)+C__m*theta__m*(int(i__m1(t), t = 0 .. t__1)+int(i__m2(t), t = 0 .. t__2))/(t__1+t__2)

i__d(t) = (-(-c*t^2*theta__d^2+b*t*theta__d^2+2*c*t*theta__d-b*theta__d+theta__d^2-2*c)*a*N^alpha*exp(theta__d*t)/theta__d^3+(-c*t__3^2*theta__d^2+b*t__3*theta__d^2+2*c*t__3*theta__d-b*theta__d+theta__d^2-2*c)*a*N^alpha*exp(theta__d*t__3)/theta__d^3)*exp(-theta__d*t)

TC__d1 := A__d*m/(t__1+t__2)+m*(int(h__d*(i__d*t+1)*i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__d*I__OD*m*n*(-(1/3)*a*c*N^alpha*N^3+(1/2)*a*b*N^alpha*N^2+a*N^alpha*N)/(t__1+t__2)+P__m*theta__m*m*(int(i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__m*I__c*m*(int(i__d(t), t = M .. t__3))/(t__1+t__2)-P__d*I__e*m*(-(1/3)*a*c*N^alpha*M^3+(1/2)*a*b*N^alpha*M^2+a*N^alpha*M)/(t__1+t__2)

TC__d2 := A__d*m/(t__1+t__2)+m*(int(h__d*(i__d*t+1)*i__d(t), t = 0 .. t__3))/(t__1+t__2)+P__d*I__OD*m*n*(-(1/3)*a*c*N^alpha*N^3+(1/2)*a*b*N^alpha*N^2+a*N^alpha*N)/(t__1+t__2)+P__m*theta__m*m*(int(i__d(t), t = 0 .. t__3))/(t__1+t__2)-P__d*I__e*m*(-(1/4)*a*c*N^alpha*t__3^4+(1/3)*a*b*N^alpha*t__3^3+(1/2)*a*N^alpha*t__3^2+M-t__3-(1/3)*a*c*N^alpha*t__3^3+(1/2)*a*b*N^alpha*t__3^2+a*N^alpha*t__3)/(t__1+t__2)

i__r(t) = (-(-c*t^2*theta__r^2+b*t*theta__r^2+2*c*t*theta__r-b*theta__r+theta__r^2-2*c)*a*N^alpha*exp(theta__r*t)/theta__r^3+(-c*t__4^2*theta__r^2+b*t__4*theta__r^2+2*c*t__4*theta__r-b*theta__r+theta__r^2-2*c)*a*N^alpha*exp(theta__r*t__4)/theta__r^3)*exp(-theta__r*t)

TC__r1 := A__r*m*n/(t__1+t__2)+m*n*(int(h__r*(i__r*t+1)*i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*theta__r*m*n*(int(i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*I__c*m*n*(int(i__r(t), t = N .. t__4))/(t__1+t__2)-P__r*I__e*m*n*(-(1/4)*a*c*N^alpha*N^4+(1/3)*a*b*N^alpha*N^3+(1/2)*a*N^alpha*N^2)/(t__1+t__2)

TC__r2 := A__r*m*n/(t__1+t__2)+m*n*(int(h__r*(i__r*t+1)*i__r(t), t = 0 .. t__4))/(t__1+t__2)+P__d*theta__r*m*n*(int(i__r(t), t = 0 .. t__4))/(t__1+t__2)-P__r*I__e*m*n*(-(1/4)*a*c*N^alpha*t__4^4+(1/3)*a*b*N^alpha*t__4^3+(1/2)*a*N^alpha*t__4^2+N-t__4-(1/3)*a*c*N^alpha*t__4^3+(1/2)*a*b*N^alpha*t__4^2+a*N^alpha*t__4)/(t__1+t__2)

TCS__1 := TC__m+TC__d1+TC__r1

TCS__2 := TC__m+TC__d1+TC__r2

TCS__3 := TC__m+TC__d2+TC__r1

TCS__4 := TC__m+TC__d2+TC__r2

 

Thanks in advance.


doubt_1.mw

Hi, I am trying to solve two simultaneous equations (for t1) they are as follows-

eq 1

i__m2(0) = (-(-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(0)*a*N^alpha/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3+(-c*t__2^2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+b*t__2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+2*c*t__2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__2)*a*N^alpha/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3)*exp(0)

eq 2

i__m1(t__1) = ((-c*t__1^2*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+b*t__1*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2+2*c*t__1*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*exp(`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__1)*a*N^alpha*(lambda-1)/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3-(-b*`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`+`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^2-2*c)*a*N^alpha*(lambda-1)/`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`^3)*exp(-`#msub(mi("&theta;",fontstyle = "normal"),mi("m"))`*t__1)

rhs(i__m2(0) = (-(-b*theta__m+theta__m^2-2*c)*exp(0)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3)*exp(0)) = rhs(i__m1(t__1) = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1))

solve({-(-b*theta__m+theta__m^2-2*c)*a*N^alpha/theta__m^3+(-c*t__2^2*theta__m^2+b*t__2*theta__m^2+2*c*t__2*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__2)*a*N^alpha/theta__m^3 = ((-c*t__1^2*theta__m^2+b*t__1*theta__m^2+2*c*t__1*theta__m-b*theta__m+theta__m^2-2*c)*exp(theta__m*t__1)*a*N^alpha*(lambda-1)/theta__m^3-(-b*theta__m+theta__m^2-2*c)*a*N^alpha*(lambda-1)/theta__m^3)*exp(-theta__m*t__1)}, [t__1]);
Warning, solutions may have been lost
 

Can someone, please help. Thanks in advance.

Dear All.

I hope we are all staying safe.

Please I want to solve Sine Gordon Equation using a numerical method I constructed (non-classical), I need to compare the result of the method with the exact solution to generate the errors. However, since the exact solution has two variables, x, and t, I really don't know how to accommodate the two in my coding.

Can someone be of help in this regard?

Thank you and kind regards

 


Download Discretization_of_Sine_Gordon_Equation.mw

Download Sine_Gordon_Implementation_Trial.mw

 

I am a little confused by why this error occurs in the second line and not the first, as well as the weird details specified in it. I don't know if the commands that are being called are inbuilt or not, but it is a safe bet that they will be. thankyou.


 

MAX := max({[seq(seq(n-(n^k-floor(n^(1/k))^(k-1)*igcd(floor(ithprime(n)^k/n^k), floor(n^(1/k))))^(1/k), n = 2 .. 100), k = 2 .. 100)][]}):

seq(seq(piecewise(radnormal(n-(n^k-floor(n^(1/k))^(k-1)*igcd(floor(ithprime(n)^k/n^k), floor(n^(1/k))))^(1/k)) = MAX, [n, k], NULL), n = 2 .. 100), k = 2 .. 100)

Error, (in radnormal/rational/nthpower) cannot determine if this expression is true or false: iroot(646162507019111437893207695980096110233782566593779/(_c27_37*_c25_38), [_c25_38, 1]) < 0

 

``


 

Download ASKMAPLE000.mw

Please, l need assistance on maplesoft activation code 

 

This is my code:

 

NEUZMinus:= proc(Unten, Oben, f,G,Liste,n)::real;
  #Unten:= Untere Intervallgrenze; Oben:= Obere Intervallgrenze; f:= zu integrierende Funktion;
  #G:= Gewicht; n:= Hinzuzufügende Knoten;
  local i;
  with(LinearAlgebra);     
  with(ListTools);
  Basenwechsel:=proc(Dividend, m);
 
  print(Anfang,Dividend,p[m]);
  Koeffizient:=quo(Dividend, p[m],x);

  Rest:=rem(Dividend, p[m],x);
 
  if m=0 then
    Basenwechsel:=[Koeffizient];
  else

    Basenwechsel:=[Koeffizient,op(Basenwechsel(Rest,m-1))];
   
  end if;
 
  end proc;
p[-1]:=0;
p[0]:=1;
for i from 1 to (numelems(Liste)+n)*2 do
  p[i]:=(x^i-add(int(x^i*p[j]*diff(G,x),x=Unten..Oben)*p[j]/int(p[j]^2*diff(G,x),x=Unten..Oben),j=0..i-1));
  print(p[i]);
c[i-1]:=coeff(p[i],x,i)/coeff(p[i-1],x,i-1);
d[i-1]:=(coeff(p[i],x,(i-1))-coeff(p[i-1],x,(i-2)))/coeff(p[i-1],x,(i-1));
if i <> 1 then
  e[i-1]:=coeff(p[i]-(c[i-1]*x+d[i-1])*p[i-1],x,i-2)/coeff(p[i-2],x,i-2);
else
  e[i-1]:=0;
end if;
end do;
print(Liste[1],numelems(Liste));
Hn:=mul(x-Liste[i],i=1..numelems(Liste));
print(Hn);
 Koeffizienten:=Reverse(Basenwechsel(Hn,n)); #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print(Koeffizienten,HIER);


print(c,d,e);
a[0][0]:=1;
a[1][0]:=x;
a[1][1]:=-e[1]*c[0]/c[1]+(d[0]-d[1]*c[0]/c[1])*x+c[0]/c[1]*x^2;
for s from 2 to numelems(Liste)+n do
  a[s][0]:=x^s;
  a[s][1]:=-e[s]*c[0]/c[s]*x^(s-1)+(d[0]-d[s]*c[0]/c[s])*x^s+c[0]/c[s]*x^(s+1);
    print (coeff(a[s][1],x,s),as1s);
end do;
for s from 2 to numelems(Liste)+n do
  for j from 2 to s do
    
      print(c[j-1]*sum(coeff(a[s][j-1],x,k-1)/c[k-1]*x^k,k=abs(s-j)+2..s+j));  print(sum((d[j-1]-c[j-1]*d[k]/c[k])*coeff(a[s][j-1],x,k)*x^k,k=abs(s-j)+1..s+j-1));  print(c[j-1]*sum(e[k+1]*coeff(a[s][j-1],x,k+1)/c[k+1]*x^k,k=abs(s-j)..s+j-2));print(e[j-1]*sum(coeff(a[s][j-2],x,k)*x^k,k=s-j+2..s+j-2));

     a[s][j]:=c[j-1]*sum(coeff(a[s][j-1],x,k-1)/c[k-1]*x^k,k=abs(s-j)+2..s+j)+sum((d[j-1]-c[j-1]*d[k]/c[k])*coeff(a[s][j-1],x,k)*x^k,k=abs(s-j)+1..s+j-1)-c[j-1]*sum(e[k+1]*coeff(a[s][j-1],x,k+1)/c[k+1]*x^k,k=abs(s-j)..s+j-2)+e[j-1]*sum(coeff(a[s][j-2],x,k)*x^k,k=abs(s-j)+2..s+j-2);

      
   
    
  end do;
end do;
for s from 0 to numelems(Liste)-1 do
  for j from 0 to s do
    print(a[s][j], Polynom[s][j]);
  end do;
end do;
M:=Matrix(n,n);
V:=Vector(n);
 
  for s from 0 to n-1 do
    for j from 0 to s do
      M(s+1,j+1):=sum(coeff(a[s][j],x,k)*Koeffizienten[k+1],k=0..n);
      if s<>j then
        M(j+1,s+1):=M(s+1,j+1);
      end if;
      print(M,1);
    end do;
    print(testb1);print(coeff(a[n][s],x,2));print(Koeffizienten[3]);print(testb2);
    V(s+1):=-sum(coeff(a[n][s],x,k)*Koeffizienten[k+1],k=0..n);
    
    print(M,V);
  end do;
print(M,V);
K:=LinearSolve(M,V);
K(n+1):=1;
print(K);

print(test2,coeff(a[max(3,2)][min(1,2)],x,2));
print(Koeffizienten[3]);
for l from 0 to n do
  for m from 0 to numelems(Liste)do
    print(Koeffizienten[m+1]*coeff(a[7][l],x,m),a[7][l],m,Koeff,Koeffizienten[m+1])
  end do;
end do;
for l from 0 to n do
  print(K(l+1)*add(Koeffizienten[m+1]*coeff(a[max(k,l)][min(k,l)],x,m),m=0..numelems(Liste)));
end do;
    nNeu:=add(p[k]*add(K(l+1)*add(Koeffizienten[m+1]*coeff(a[max(k,l)][min(k,l)],x,m),m=0..numelems(Liste)),l=0..n),k=numelems(Liste)..numelems(Liste)+n);
fsolve(nNeu);
Em:=add(p[i]*K[i+1],i=0..n);
Hnm:=Hn*Em;
KnotenHnm:=fsolve(Hnm);
print(Hn,alt,Em,neu,Hnm);
print(Testergebnis,nNeu);
print(fsolve(Hnm),fsolve(nNeu));
KoeffizientenHnm:=Reverse(Basenwechsel(Hnm,n+numelems(Liste)));  #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print(KoeffizientenHnm);
h0:=int(diff(G,x),x=Unten..Oben);
b[n+numelems(Liste)+2]:=0;
b[n+numelems(Liste)+1]:=0;
  for i from 1 to n+numelems(Liste) do
    for j from n+numelems(Liste) by -1 to 1 do
      print(test21);
      b[j]:=KoeffizientenHnm[j]+(d[j]+KnotenHnm[i]*c[j])*b[j+1]+e[j+1]*b[j+2];
  print(test22);
    end do;
    print(test23);
    gxi:=quo(Hnm,x-KnotenHnm[i],x);
   print(test24);
    Gewichte[i]:=c[1]*b[2]*h0/gxi(i);
   
    Delta[i]:=c[1]*b[2];
  end do;
print(KnotenHnm);
print(Gewichte);
sum(Knoten[k]*Gewichte[k],k=1..n+numelems(Liste));
end proc

With the first use of the subprocedure Basenwechsel, everything works fine. With the input

NEUZMinus(-1,1,x,x,[-sqrt(3/5),0,sqrt(3/5)],4)

I get the result [0,0,0,1,0] correctly.

The following time I use it, the polynomial is different, and m is 7 in that case, so the list should have 8 entries, it just returns the same [0,0,0,1,0] again, however. Changing the polynomial in the first application to say 5*Hn results in [0,0,0,5,0] in both cases again. The procedure seems to have saved the old values and never overwrites them. How can I fix this? I have highlighted the use of the procedure with exclamation marks.

 

Thank you in advance!

P.S.: The lengthy result is this:

NEUZMinus(-1,1,x,x,[-sqrt(3/5),0,sqrt(3/5)],4)

                               x
                              2   1
                             x  - -
                                  3
                             3   3  
                            x  - - x
                                 5  
                          4   3    6  2
                         x  + -- - - x
                              35   7   
                        5   5      10  3
                       x  + -- x - -- x
                            21     9    
                     6    5    5   2   15  4
                    x  - --- + -- x  - -- x
                         231   11      11   
                   7   35      105  3   21  5
                  x  - --- x + --- x  - -- x
                       429     143      13   
                8    7     28   2   14  4   28  6
               x  + ---- - --- x  + -- x  - -- x
                    1287   143      13      15   
              9    63      84   3   126  5   36  7
             x  + ---- x - --- x  + --- x  - -- x
                  2431     221      85       17   
         10    63     315   2   210  4   630  6   45  8
        x   - ----- + ---- x  - --- x  + --- x  - -- x
              46189   4199      323      323      19   
         11    33      55   3   330  5   330  7   55  9
        x   - ---- x + --- x  - --- x  + --- x  - -- x
              4199     323      323      133      21   
    12    33     198   2   2475  4   660  6   495  8   66  10
   x   + ----- - ---- x  + ---- x  - --- x  + --- x  - -- x  
         96577   7429      7429      437      161      23    
 13    429       2574   3   1287  5   1716  7   429  9   78  11
x   + ------ x - ----- x  + ---- x  - ---- x  + --- x  - -- x  
      185725     37145      2185      805       115      25    
     14     143      1001   2   1001  4   1001  6   1001  8
    x   - ------- + ------ x  - ---- x  + ---- x  - ---- x
          1671525   111435      6555      1035      345    

         1001  10   91  12
       + ---- x   - -- x  
         225        27    
                           1   (1/2)   
                         - - 15     , 3
                           5           
               /    1   (1/2)\   /    1   (1/2)\
               |x + - 15     | x |x - - 15     |
               \    5        /   \    5        /
           /    1   (1/2)\   /    1   (1/2)\   4   3    6  2
   Anfang, |x + - 15     | x |x - - 15     |, x  + -- - - x
           \    5        /   \    5        /       35   7   
                            3   3     3   3  
                   Anfang, x  - - x, x  - - x
                                5         5  
                                   2   1
                       Anfang, 0, x  - -
                                       3
                          Anfang, 0, x
                          Anfang, 0, 1
                     [0, 0, 0, 1, 0], HIER #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                            c, d, e
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                            0, as1s
                           4   2    4
                           -- x  + x
                           15        
                               0
                            4    9   2
                          - -- - -- x
                            45   35   
                               1  2
                             - - x
                               3   
                           9   3    5
                           -- x  + x
                           35        
                               0
                          12      16  3
                        - --- x - -- x
                          175     63   
                               1  3
                             - - x
                               3   
                      12   2   8   4    6
                      --- x  + -- x  + x
                      175      45        
                               0
                        4     8   2   25  4
                     - --- - --- x  - -- x
                       175   175      99   
                          12   2   4   4
                        - --- x  - -- x
                          175      15   
                           16  4    6
                           -- x  + x
                           63        
                               0
                          16   2   25  4
                        - --- x  - -- x
                          245      99   
                               1  4
                             - - x
                               3   
                      16   3   40   5    7
                      --- x  + --- x  + x
                      245      231        
                               0
                     64       640   3   36   5
                  - ---- x - ----- x  - --- x
                    3675     14553      143   
                          64   3   4   5
                        - --- x  - -- x
                          945      15   
                  64   2   16   4   72   6    8
                 ---- x  + --- x  + --- x  + x
                 3675      385      455        
                               0
                64      144   2    40   4   49   6
             - ----- - ----- x  - ---- x  - --- x
               11025   13475      1001      195   
                     24   4   9   6   144   2
                   - --- x  - -- x  - ---- x
                     539      35      8575   
                           25  5    7
                           -- x  + x
                           99        
                               0
                         400   3   36   5
                       - ---- x  - --- x
                         6237      143   
                               1  5
                             - - x
                               3   
                     400   4   20   6    8
                     ---- x  + --- x  + x
                     6237      117        
                               0
                    80   2    500   4   49   6
                 - ---- x  - ----- x  - --- x
                   4851      11583      195   
                          20   4   4   6
                        - --- x  - -- x
                          297      15   
                  80   3    40   5   7   7    9
                 ---- x  + ---- x  + -- x  + x
                 4851      1001      45        
                               0
                64        640   3   28   5   64   7
             - ----- x - ----- x  - --- x  - --- x
               14553     63063      715      255   
                     4   5   9   7    80   3
                   - -- x  - -- x  - ---- x
                     91      35      4851   
           64    2    640   4   16   6   160   8    10
          ----- x  + ----- x  + --- x  + ---- x  + x  
          14553      63063      455      1071         
                               0
           64      128   2    80   4   224   6   81   8
        - ----- - ----- x  - ---- x  - ---- x  - --- x
          43659   49049      9009      5967      323   
               640   4   16   6   16  8    1280   2
            - ----- x  - --- x  - -- x  - ------ x
              63063      405      63      305613   
                          36   6    8
                          --- x  + x
                          143        
                               0
                         100   4   49   6
                       - ---- x  - --- x
                         1573      195   
                               1  6
                             - - x
                               3   
                     100   5   28   7    9
                     ---- x  + --- x  + x
                     1573      165        
                               0
                   1600   3   336   5   64   7
                 - ----- x  - ---- x  - --- x
                   99099      7865      255   
                          48   5   4   7
                        - --- x  - -- x
                          715      15   
                1600   4   28   6   144  8    10
                ----- x  + --- x  + --- x  + x  
                99099      715      935         
                               0
              320   2    140   4   2352   6   81   8
           - ----- x  - ----- x  - ----- x  - --- x
             77077      14157      60775      323   
                    12   6   9   8    180   4
                  - --- x  - -- x  - ----- x
                    275      35      11011   
           320   3    320   5   32   7   216   9    11
          ----- x  + ----- x  + --- x  + ---- x  + x  
          77077      33033      935      1463         
                               0
       256        5120    3    1152   5    4608   7   100  9
    - ------ x - ------- x  - ------ x  - ------ x  - --- x
      231231     2081079      133705      124355      399   
               64   5   256   7   16  9    25600   3
            - ---- x  - ---- x  - -- x  - ------- x
              6435      6545      63      6243237   
   256    2    320    4    1280   6    800   8   100  10    12
  ------ x  + ------ x  + ------ x  + ----- x  + --- x   + x  
  231231      127413      153153      24871      693          
                               0
   256      64    2    32000    4    1120   6    900   8   121  10
- ------ - ----- x  - -------- x  - ------ x  - ----- x  - --- x  
  693693   99099      15162147      138567      24871      483    
       8000    4    160   6    600   8   25  10    8000    2
    - ------- x  - ----- x  - ----- x  - -- x   - ------- x
      3270267      18513      16093      99       7630623   
                          49   7    9
                          --- x  + x
                          195        
                               0
                         588   5   64   7
                       - ---- x  - --- x
                         9295      255   
                               1  7
                             - - x
                               3   
                     588   6   112  8    10
                     ---- x  + --- x  + x  
                     9295      663         
                               0
                   980   4    5488   6   81   8
                - ----- x  - ------ x  - --- x
                  61347      129285      323   
                         196   6   4   8
                       - ---- x  - -- x
                         2925      15   
               980   5   2352   7   189   9    11
              ----- x  + ----- x  + ---- x  + x  
              61347      60775      1235         
                               0
            2240   3    84672   5    4032   7   100  9
         - ------ x  - ------- x  - ------ x  - --- x
           552123      8690825      104975      399   
                     48   7   9   9    756   5
                  - ---- x  - -- x  - ----- x
                    1105      35      46475   
         2240   4    896   6    7776   8   40   10    12
        ------ x  + ----- x  + ------ x  + --- x   + x  
        552123      94809      230945      273          
                               0
      64    2    22400   4    127008   6   1080   8   121  10
   - ----- x  - ------- x  - -------- x  - ----- x  - --- x  
     61347      9386091      15011425      29393      483    
              1792   6    48   8   16  10    2240   4
           - ------ x  - ---- x  - -- x   - ------ x
             182325      1235      63       552123   
  64    3    22400   5    1120   7    600   9   385   11    13
 ----- x  + ------- x  + ------ x  + ----- x  + ---- x   + x  
 61347      9386091      138567      19019      2691          
                               0
    256        51200    3    13440   5    2560   7    5500   9
 - ------ x - -------- x  - ------- x  - ------ x  - ------ x
   920205     84474819      6605027      323323      153387   

      144  11
    - --- x  
      575    
      22400   5    4320   7   1000   9   25  11    56000    3
   - ------- x  - ------ x  - ----- x  - -- x   - -------- x
     9386091      508079      27027      99       54660177   
  256    2     7168    4    13440   6    80000    8   100   10
 ------ x  + -------- x  + ------- x  + -------- x  + ---- x  
 920205      11471889      6605027      10669659      3289    

      504   12    14
    + ---- x   + x  
      3575          
                               0
    256       3072    2    112000    4    112000   6    8100    8
- ------- - -------- x  - --------- x  - -------- x  - ------- x
  2760615   19119815      217965891      59445243      1062347   

     264   10   169  12
   - ---- x   - --- x  
     7475       675    
     89600    4    13440   6    21600   8   140   10   36   12
 - --------- x  - ------- x  - ------- x  - ---- x   - --- x  
   149134557      6605027      2719717      3887       143    

        768    2
    - ------- x
      2924207   
                        1, Polynom[0][0]
                        x, Polynom[1][0]
                     1    2               
                     - + x , Polynom[1][1]
                     3                    
                        2               
                       x , Polynom[2][0]
                    4       3               
                    -- x + x , Polynom[2][1]
                    15                      
                 4   2    4   4                
                 -- x  + x  + --, Polynom[2][2]
                 21           45               
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                              16
                              ---
                              245
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
             Matrix(%id = 18446745693991291350), 1
                             testb1
                               0
                               0
                             testb2
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
          Matrix(%id = 18446745693991291350),

            Vector[column](%id = 18446745693991291470)
           Vector[column](%id = 18446745693991291830)
                                  9
                           test2, --
                                  35
                               0
                           7             
                       0, x , 0, Koeff, 0
                           7             
                       0, x , 1, Koeff, 0
                           7             
                       0, x , 2, Koeff, 0
                           7             
                       0, x , 3, Koeff, 1
                     49   6    8             
                  0, --- x  + x , 0, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 1, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 2, Koeff, 0
                     195                     
                     49   6    8             
                  0, --- x  + x , 3, Koeff, 1
                     195                     
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 0, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 1, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 2, Koeff, 0
                663           9295                
                112  7    9   588   5             
             0, --- x  + x  + ---- x , 3, Koeff, 1
                663           9295                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 0, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 1, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 2, Koeff, 0
         60775      1235            61347                
         2352   6   189   8    10    980   4             
      0, ----- x  + ---- x  + x   + ----- x , 3, Koeff, 1
         60775      1235            61347                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 0, Koeff, 0
   94809      230945      273            552123                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 1, Koeff, 0
   94809      230945      273            552123                
    896   5    7776   7   40   9    11    2240   3             
0, ----- x  + ------ x  + --- x  + x   + ------ x , 2, Koeff, 0
   94809      230945      273            552123                
   2240    896   5    7776   7   40   9    11    2240   3     
  ------, ----- x  + ------ x  + --- x  + x   + ------ x , 3,
  552123  94809      230945      273            552123        

    Koeff, 1
                               0
                               0
                               0
                               0
                               0
/    1   (1/2)\   /    1   (1/2)\       155   10  2    4       
|x + - 15     | x |x - - 15     |, alt, --- - -- x  + x , neu,
\    5        /   \    5        /       891   9                

  /    1   (1/2)\   /    1   (1/2)\ /155   10  2    4\
  |x + - 15     | x |x - - 15     | |--- - -- x  + x |
  \    5        /   \    5        / \891   9         /
 Testergebnis,

      2459840   5    80254400        188027200   3    2240   7
   - --------- x  - ----------- x + ----------- x  + ------ x
     193795173      44766684963     19185722127      552123   
-0.9604912687, -0.7745966692, -0.4342437493, 0., 0.4342437493,

  0.7745966692, 0.9604912687, -1.435338337, -0.8946894490,

  -0.5176357564, 0., 0.5176357564, 0.8946894490, 1.435338337
                        [0, 0, 0, 1, 0] #!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
                             test21
Error, (in NEUZMinus) invalid subscript selector

 

Doing a routine simplification but got an error...Dont know where the mistake comes from.

 

simplification_error.mw

Dear All.

Please kindly help to correct the attached code on discretization of fourth order PDE using method of line.
Thank you and kind regards.

restart

``

``

Discretization of parabolic equation with method of line

diff(u(x, t), t) = -2*(diff(diff(u(x, t), x), x))-(diff(diff(diff(diff(u(x, t), x), x), x), x))-u(x, t)*(diff(u(x, t), x))

u(x, t)

u(x, t)

u(x, 0) = 0.3e-1*sin(x)

8

``

``

``

Convert the BC to finite difference

(1/2)*(u[m+1](t)-u[m-1](t))/h

(u[m-1](t)-2*u[m](t)+u[m+1](t))/h^2

(u[m-2](t)-4*u[m-1](t)+6*u[m](t)-4*u[m+1](t)+u[m+2](t))/h^4

````

Convert the governing equation to finite difference form

Error, invalid input: diff received 2*h, which is not valid for its 2nd argument

Error, invalid input: diff received 2*h, which is not valid for its 2nd argument

Error, invalid input: LinearAlgebra:-GenerateMatrix expects its 1st argument, eqns, to be of type ({list, set})({`=`, algebraic}), but received eqs

A

``


 

Download Discretization_of_PDE_Order_4.mw

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